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700 (number)

## Summary

700 (seven hundred) is the natural number following 699 and preceding 701.

 ← 699 700 701 →
Cardinalseven hundred
Ordinal700th
(seven hundredth)
Factorization22 × 52 × 7
Greek numeralΨ´
Roman numeralDCC
Binary10101111002
Ternary2212213
Octal12748
Duodecimal4A412

It is the sum of four consecutive primes (167 + 173 + 179 + 181), the perimeter of a Pythagorean triangle (75 + 308 + 317)[1] and a Harshad number.

## Integers from 701 to 799

Nearly all of the palindromic integers between 700 and 800 are used as model numbers for Boeing Commercial Airplanes, and the only one not officially used by Boeing, 797, is commonly speculated to be the number of the next new Boeing commercial airplane.[2]

### 710s

• 710 = 2 × 5 × 71, sphenic number, nontotient, number of forests with 11 vertices [10][11]
• 711 = 32 × 79, Harshad number, number of planar Berge perfect graphs on 7 nodes.[12] Also the phone number of Telecommunications Relay Service, commonly used by the deaf and hard-of-hearing.
• 712 = 23 × 89, sum of the first twenty-one primes, totient sum for first 48 integers. It is the largest known number such that it and its 8th power (66,045,000,696,445,844,586,496) have no common digits.
• 713 = 23 × 31, blum integer, main area code for Houston, TX. In Judaism there is 713 letters on a Mezuzah scroll.
• 714 = 2 × 3 × 7 × 17, sum of twelve consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83), nontotient, balanced number,[13] member of Ruth–Aaron pair (either definition); area code for Orange County, California.
• 714 is the number of career home runs hit by Babe Ruth, a record that stood from his last home run on May 25, 1935, until being broken by Hank Aaron on April 8, 1974.
• Flight 714 to Sidney is a Tintin graphic novel.
• 714 is the badge number of Sergeant Joe Friday.
• 715 = 5 × 11 × 13, sphenic number, pentagonal number,[14] pentatope number ( binomial coefficient ${\displaystyle {\tbinom {13}{4}}}$  ),[15] Harshad number, member of Ruth-Aaron pair (either definition)
• The product of 714 and 715 is the product of the first 7 prime numbers (2, 3, 5, 7, 11, 13, and 17)
• 716 = 22 × 179, area code for Buffalo, NY
• 717 = 3 × 239, palindromic number, model number for the Boeing 717
• 718 = 2 × 359, area code for Brooklyn, NY and Bronx, NY
• 719 = prime number, factorial prime (6! − 1),[16] Sophie Germain prime,[17] safe prime,[18] sum of seven consecutive primes (89 + 97 + 101 + 103 + 107 + 109 + 113), Chen prime, Eisenstein prime with no imaginary part

### 740s

• 740 = 22 × 5 × 37, nontotient, number of connected squarefree graphs on 9 nodes [38]
• 741 = 3 × 13 × 19, sphenic number, triangular number[4]
• 742 = 2 × 7 × 53, sphenic number, decagonal number,[39] icosahedral number. It is the smallest number that is one more than triple its reverse. Lazy caterer number (sequence A000124 in the OEIS). Number of partitions of 30 into divisors of 30.[40]
• 743 = prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part
• 744 = 23 × 3 × 31, sum of four consecutive primes (179 + 181 + 191 + 193). It is the coefficient of the first degree term of the expansion of Klein's j-invariant. Furthermore, 744 =3 × 248 where 248 is the dimension of the Lie algebra E8.
• 745 = 5 × 149 = 24 + 36, number of non-connected simple labeled graphs covering 6 vertices[41]
• 746 = 2 × 373 = 15 + 24 + 36 = 17 + 24 + 36, nontotient, number of non-normal semi-magic squares with sum of entries equal to 6[42]
• 747 = 32 × 83 = ${\displaystyle \lfloor {\frac {4^{23}}{3^{23}}}\rfloor }$ ,[43] palindromic number, model number of the Boeing 747 jet airliner
• 748 = 22 × 11 × 17, nontotient, happy number, primitive abundant number[44]
• 749 = 7 × 107, sum of three consecutive primes (241 + 251 + 257), blum integer

### 750s

• 750 = 2 × 3 × 53, enneagonal number.[45]
• 751 = prime number, Chen prime
• 752 = 24 × 47, nontotient, number of partitions of 11 into parts of 2 kinds[46]
• 753 = 3 × 251, blum integer
• 754 = 2 × 13 × 29, sphenic number, nontotient, totient sum for first 49 integers, number of different ways to divide a 10 × 10 square into sub-squares [47]
• 755 = 5 × 151, number of vertices in a regular drawing of the complete bipartite graph Kn,n.[48] In 1976, Major League Baseball player Hank Aaron ended his career with a Major League record 755 home runs (record now held by Barry Bonds).
• 756 = 22 × 33 × 7, sum of six consecutive primes (109 + 113 + 127 + 131 + 137 + 139), pronic number,[3] Harshad number
• 757 = prime number, palindromic prime, sum of seven consecutive primes (97 + 101 + 103 + 107 + 109 + 113 + 127), happy number, model number for the Boeing 757
• 758 = 2 × 379, nontotient, prime number of measurement [49]
• 759 = 3 × 11 × 23, sphenic number, sum of five consecutive primes (139 + 149 + 151 + 157 + 163), a q-Fibonacci numbers for q=3 [50]

### 780s

• 780 = 22 × 3 × 5 × 13, sum of four consecutive primes in a quadruplet (191, 193, 197, and 199); sum of ten consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101), triangular number,[4] hexagonal number,[5] Harshad number
• 780 and 990 are the fourth smallest pair of triangular numbers whose sum and difference (1770 and 210) are also triangular.
• 781 = 11 × 71, sum of powers of 5/repdigit in base 5 (11111), Mertens function(781) = 0, lazy caterer number (sequence A000124 in the OEIS)
• 782 = 2 × 17 × 23, sphenic number, nontotient, pentagonal number,[14] Harshad number, also, 782 gear used by U.S. Marines
• 783 = 33 × 29, heptagonal number
• 784 = 24 × 72 = 282 = ${\displaystyle 1^{3}+2^{3}+3^{3}+4^{3}+5^{3}+6^{3}+7^{3}}$ , the sum of the cubes of the first seven integers, happy number
• 785 = 5 × 157, Mertens function(785) = 0, number of series-reduced planted trees with 6 leaves of 2 colors [68]

## References

1. ^ Sloane, N. J. A. (ed.). "Sequence A024364 (Ordered perimeters of primitive Pythagorean triangles)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
2. ^ "The Boeing 797 - Here Are The Clues We Have So Far". Simple Flying. 2020-03-04. Retrieved 2021-04-06.
3. ^ a b "Sloane's A002378 : Oblong (or promic, pronic, or heteromecic) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
4. ^ a b c "Sloane's A000217 : Triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
5. ^ a b "Sloane's A000384 : Hexagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
6. ^ "Sloane's A006886 : Kaprekar numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
7. "Sloane's A006753 : Smith numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
8. ^ Sloane, N. J. A. (ed.). "Sequence A026671 (Number of lattice paths from (0,0) to (n,n) with steps (0,1), (1,0) and, when on the diagonal, (1,1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-22.
9. ^ Sloane, N. J. A. (ed.). "Sequence A002865 (Number of partitions of n that do not contain 1 as a part)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
10. ^ Hougardy, Stefan (6 October 2006). "Classes of perfect graphs - ScienceDirect". Discrete Mathematics. Creation and Recreation: A Tribute to the Memory of Claude Berge. 306 (19): 2529–2571. doi:10.1016/j.disc.2006.05.021. Retrieved 2022-05-22.
11. ^ Sloane, N. J. A. (ed.). "Sequence A005195 (Number of forests with n unlabeled nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-22.
12. ^ Sloane, N. J. A. (ed.). "Sequence A123449 (Number of planar Berge perfect graphs on n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
13. ^ Sloane, N. J. A. (ed.). "Sequence A020492 (Balanced numbers: numbers k such that phi(k) (A000010) divides sigma(k) (A000203))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
14. ^ a b "Sloane's A000326 : Pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
15. ^ "Sloane's A000332 : Binomial coefficient binomial(n,4)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
16. ^ "Sloane's A088054 : Factorial primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
17. ^ a b "Sloane's A005384 : Sophie Germain primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
18. ^ "Sloane's A005385 : Safe primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
19. ^ "Sloane's A003215 : Hex (or centered hexagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
20. ^ Sloane, N. J. A. (ed.). "Sequence A066897 (Total number of odd parts in all partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-22.
21. ^ Sloane, N. J. A. (ed.). "Sequence A001105". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
22. ^ Sloane, N. J. A. (ed.). "Sequence A016064 (Smallest side lengths of almost-equilateral Heronian triangles)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-22.
23. ^ Sloane, N. J. A. (ed.). "Sequence A003500". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-22.
24. ^ Sloane, N. J. A. (ed.). "Sequence A335025 (Largest side lengths of almost-equilateral Heronian triangles)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-22.
25. ^ "Sloane's A002411 : Pentagonal pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
26. ^ a b c d "Sloane's A031157 : Numbers that are both lucky and prime". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
27. ^ "Sloane's A047696 : Smallest positive number that can be written in n ways as a sum of two (not necessarily positive) cubes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
28. ^ Sloane, N. J. A. (ed.). "Sequence A007749 (Numbers k such that k!! - 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.
29. ^ "Sloane's A082897 : Perfect totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
30. ^ "Sloane's A016754 : Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
31. ^ Sloane, N. J. A. (ed.). "Sequence A004123 (Number of generalized weak orders on n points)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-22.
32. ^ Sloane, N. J. A. (ed.). "Sequence A007317 (Binomial transform of Catalan numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
33. ^ Sloane, N. J. A. (ed.). "Sequence A306445 (Number of collections of subsets of {1, 2, ..., n} that are closed under union and intersection)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-22.
34. ^ "Sloane's A006562 : Balanced primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
35. ^ Sloane, N. J. A. (ed.). "Sequence A057864 (Number of simple traceable graphs on n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-22.
36. ^ "Sloane's A069099 : Centered heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
37. ^ "Sloane's A016038 : Strictly non-palindromic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
38. ^ Sloane, N. J. A. (ed.). "Sequence A077269 (Number of connected squarefree graphs on n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-23.
39. ^ "Sloane's A001107 : 10-gonal (or decagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
40. ^ Sloane, N. J. A. (ed.). "Sequence A018818 (Number of partitions of n into divisors of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
41. ^ Sloane, N. J. A. (ed.). "Sequence A327070 (Number of non-connected simple labeled graphs covering n vertices)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-23.
42. ^ Sloane, N. J. A. (ed.). "Sequence A321719 (Number of non-normal semi-magic squares with sum of entries equal to n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-30.
43. ^ Sloane, N. J. A. (ed.). "Sequence A064628 (Floor(4^n / 3^n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-30.
44. ^ "Sloane's A091191 : Primitive abundant numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
45. ^ "Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
46. ^ Sloane, N. J. A. (ed.). "Sequence A000712". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-30.
47. ^ Sloane, N. J. A. (ed.). "Sequence A034295 (Number of different ways to divide an n X n square into sub-squares)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-23.
48. ^ Sloane, N. J. A. (ed.). "Sequence A331755 (Number of vertices in a regular drawing of the complete bipartite graph K_{n,n})". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-23.
49. ^ Sloane, N. J. A. (ed.). "Sequence A002049 (Prime numbers of measurement)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-23.
50. ^ Sloane, N. J. A. (ed.). "Sequence A015474". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-23.
51. ^ "Sloane's A005448 : Centered triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
52. ^ "Sloane's A001844 : Centered square numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
53. ^ Sloane, N. J. A. (ed.). "Sequence A036469 (Partial sums of A000009 (partitions into distinct parts))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
54. ^ Sloane, N. J. A. (ed.). "Sequence A001189 (Number of degree-n permutations of order exactly 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-23.
55. ^ "Sloane's A000085 : Number of self-inverse permutations on n letters, also known as involutions". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
56. ^ Sloane, N. J. A. (ed.). "Sequence A002414 (Octagonal pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-23.
57. ^ "Sloane's A005891 : Centered pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
58. ^ Sloane, N. J. A. (ed.). "Sequence A007283". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-30.
59. ^ "Sloane's A080076 : Proth primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
60. ^ Sloane, N. J. A. (ed.). "Sequence A162862 (Numbers n such that n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-30.
61. ^ Sloane, N. J. A. (ed.). "Sequence A085150 (Numbers n such that n!!!!!!+1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-30.
62. ^ "Sloane's A000078 : Tetranacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
63. ^ "Sloane's A005282 : Mian-Chowla sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
64. ^ (sequence A033453 in the OEIS)
65. ^ Posner, Eliezer. "On the Meaning of Three". Chabad. Retrieved 2 July 2016.
66. ^ Dennis, Geoffrey. "Judaism & Numbers". My Jewish Learning. Retrieved 2 July 2016.
67. ^ "Sloane's A100827 : Highly cototient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
68. ^ Sloane, N. J. A. (ed.). "Sequence A050381 (Number of series-reduced planted trees with n leaves of 2 colors)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.
69. ^ Sloane, N. J. A. (ed.). "Sequence A242882 (Number of compositions of n into parts with distinct multiplicities)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.
70. ^ "Sloane's A000041 : a(n) = number of partitions of n". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
71. ^ "Sloane's A003154 : Centered 12-gonal numbers. Also star numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
72. ^ Sloane, N. J. A. (ed.). "Sequence A001550". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.
73. ^ Sloane, N. J. A. (ed.). "Sequence A000274 (Number of permutations of length n with 2 consecutive ascending pairs)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.
74. ^ Sloane, N. J. A. (ed.). "Sequence A325508 (Product of primes indexed by the prime exponents of n!)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.
75. ^ Sloane, N. J. A. (ed.). "Sequence A051885 (Smallest number whose sum of digits is n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.